If they are based in Torah, what makes them "not Torah true"? Do you know for a fact that these places don't ask for Rabinnic advice?
Torah-True implies being true to the Torah. [i don't know what is so hard for certain DDF members to understand this.] If they are true to the Torah [i.e. legitimate shitta] and they run al pi daas Torah [i.e. they make serious decisions only with rabbinic advice] then they are Torah True. But as someone else pointed out, even many "Chareidi" places have serious issues with this, Kal Vachomer a place that doesn't respect Torah Authority.
Can we accept wikipedia's definition of Modern Orthodoxy?
https://en.wikipedia.org/wiki/Modern_Orthodox_Judaism"Modern Orthodox Judaism (also Modern Orthodox or Modern Orthodoxy) is a movement within Orthodox Judaism that attempts to synthesize Jewish values and the observance of Jewish law with the secular, modern world."
I believe many, if not most Modern Orthodox schools are run under Daas Torah.
I believe that you are naďve.
Many Modern Orthodox day schools are actually under the Torah U'mesorah umbrella. My definition of who can be Daas Torah for anyone in Klal Yisroel isn't limited to 3 gedolim. I would guess that you would not consider Rav Soloveitchik to be a legitimate Daas Torah, but if you listen to the recording I referenced above, quite a few mentions are made of him in a positive light as a Talmid Chacham and a Gadol
If every modern orthodox school was run al pi the daas Torah of Rav Soleveichik the Jewish world would be in amuch better place.